Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to \(\beta\)-shifts

DOI10.5802/aif.2238zbMath1138.37008OpenAlexW2462218649MaRDI QIDQ2372774

Jaroslaw Kwapisz, Veronica Baker, Marcy M. Barge

Publication date: 1 August 2007

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2006__56_7_2213_0

zbMATH Keywords

tilingssubstitutionpure discrete spectrum spectrum

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06)

Related Items (20)

Geometrical and spectral properties of Pisot substitutions ⋮ Dynamical directions in numeration ⋮ Decidability Problems for Self-induced Systems Generated by a Substitution ⋮ Algorithm for determining pure pointedness of self-affine tilings ⋮ Conjugacy of unimodular Pisot substitution subshifts to domain exchanges ⋮ Central sets and substitutive dynamical systems ⋮ The Cech cohomology and the spectrum for 1-dimensional tiling systems ⋮ Overlap coincidence to strong coincidence in substitution tiling dynamics ⋮ Dual systems of algebraic iterated function systems ⋮ Beta-expansions, natural extensions and multiple tilings associated with Pisot units ⋮ The Pisot conjecture for -substitutions ⋮ Purely periodic \(\beta \)-expansions in the Pisot non-unit case ⋮ Geometrical models for a class of reducible Pisot substitutions ⋮ Conjugacies of model sets ⋮ Tilings for Pisot beta numeration ⋮ Homological Pisot substitutions and exact regularity ⋮ Rauzy fractals with countable fundamental group ⋮ A combinatorial approach to products of Pisot substitutions ⋮ Central sets generated by uniformly recurrent words ⋮ Pure discrete spectrum for a class of one-dimensional substitution tiling systems

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